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%I #16 Sep 28 2020 21:46:05
%S 1,1,2,4,10,22,54,120,284,626,1438,3136,7044,15212,33596,71952,156856,
%T 333610,719886,1522224,3257972,6855476,14574772,30541264,64571400,
%U 134827252,283727564,590608960,1237926184,2569953496,5368225848,11118205088,23155034480,47856472218
%N a(0) = 1; for n>0, a(n) = (n+3)*2^(n-2)-n*binomial(n-1, floor( (n-1)/2 ))-(n-1)*binomial(n-2,floor((n-2)/2)).
%H A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Rinaldi/rinaldi5.html">Permutations defining convex permutominoes</a>, J. Int. Seq. 10 (2007) # 07.9.7. [See S_{n+1}.]
%H F. Disanto and S. Rinaldi, <a href="http://puma.dimai.unifi.it/22_1/2-disanto_rinaldi.pdf">Symmetric convex permutominoes and involutions</a>, PU. M. A., Vol. 22 (2011), No. 1, pp. 39-60. - From _N. J. A. Sloane_, May 04 2012
%F Conjecture: -(n-1)*(3*n^2-27*n+56)*a(n) +2*(n-5)*(3*n^2-12*n+5)*a(n-1) +4*(3*n^3-33*n^2+110*n-118)*a(n-2) -8*(n-3)*(3*n^2-21*n+32)*a(n-3)=0. - _R. J. Mathar_, Jan 04 2017
%t Join[{1},Table[((n+3)2^(n-2))-(n Binomial[n-1,Floor[(n-1)/2]]) -((n-1)Binomial[n-2,Floor[(n-2)/2]]),{n,50}]] (* _Harvey P. Dale_, Mar 17 2011 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jul 28 2007